You can take the A+, Network+, and Security+ certifications in any sequence. The good thing about taking these three courses is that all are offered by CompTIA, which is not restricted to a particular vendor. Passing the test and getting the certification depends on your knowledge about these technologies. Since these are all basic certifications with equal complexity, neither one of these builds a knowledge base for the other. The only requirement for these courses is a basic understanding of using computers.
The only question you need to ask yourself is which CompTIA certification makes the most sense for you. There is no sure answer to which course you should take before others. It all depends on what works best for you. You can make an educated decision once you understand what each of these courses entails.